Update, Aug. 2019:
In the five years since this was first posted, science continues to grind away, answering a few questions which in turn create a bunch more questions. The Baillie tree ring / ice core team is increasingly of the opinion that the 535 – 540 AD global cooldown was caused by huge volcanic eruptions, at least two of them bracketing the period. A team including Robert A Dull published a paper August 16 entitled “Radiocarbon and geologic evidence reveal ilopango volcano as the source of the colossal ‘mystery’ eruption of 539/40 CE” that appears to nicely define the most recent end of that bracket.
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